(6x^2+4y-1)dx+(4x-9y^2)dy=0

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Solution for (6x^2+4y-1)dx+(4x-9y^2)dy=0 equation: 


Simplifying
(6x2 + 4y + -1) * dx + (4x + -9y2) * dy = 0

Reorder the terms:
(-1 + 6x2 + 4y) * dx + (4x + -9y2) * dy = 0

Reorder the terms for easier multiplication:
dx(-1 + 6x2 + 4y) + (4x + -9y2) * dy = 0
(-1 * dx + 6x2 * dx + 4y * dx) + (4x + -9y2) * dy = 0

Reorder the terms:
(-1dx + 4dxy + 6dx3) + (4x + -9y2) * dy = 0
(-1dx + 4dxy + 6dx3) + (4x + -9y2) * dy = 0

Reorder the terms for easier multiplication:
-1dx + 4dxy + 6dx3 + dy(4x + -9y2) = 0
-1dx + 4dxy + 6dx3 + (4x * dy + -9y2 * dy) = 0
-1dx + 4dxy + 6dx3 + (4dxy + -9dy3) = 0

Reorder the terms:
-1dx + 4dxy + 4dxy + 6dx3 + -9dy3 = 0

Combine like terms: 4dxy + 4dxy = 8dxy
-1dx + 8dxy + 6dx3 + -9dy3 = 0

Solving
-1dx + 8dxy + 6dx3 + -9dy3 = 0

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Factor out the Greatest Common Factor (GCF), 'd'.
d(-1x + 8xy + 6x3 + -9y3) = 0


Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

Move all terms containing d to the left, all other terms to the right.

Simplifying
d = 0

Subproblem 2
Set the factor '(-1x + 8xy + 6x3 + -9y3)' equal to zero and attempt to solve:

Simplifying
-1x + 8xy + 6x3 + -9y3 = 0

Solving
-1x + 8xy + 6x3 + -9y3 = 0

Move all terms containing d to the left, all other terms to the right.

Add 'x' to each side of the equation.
-1x + 8xy + 6x3 + x + -9y3 = 0 + x

Reorder the terms:
-1x + x + 8xy + 6x3 + -9y3 = 0 + x

Combine like terms: -1x + x = 0
0 + 8xy + 6x3 + -9y3 = 0 + x
8xy + 6x3 + -9y3 = 0 + x
Remove the zero:
8xy + 6x3 + -9y3 = x

Add '-8xy' to each side of the equation.
8xy + 6x3 + -8xy + -9y3 = x + -8xy

Reorder the terms:
8xy + -8xy + 6x3 + -9y3 = x + -8xy

Combine like terms: 8xy + -8xy = 0
0 + 6x3 + -9y3 = x + -8xy
6x3 + -9y3 = x + -8xy

Add '-6x3' to each side of the equation.
6x3 + -6x3 + -9y3 = x + -8xy + -6x3

Combine like terms: 6x3 + -6x3 = 0
0 + -9y3 = x + -8xy + -6x3
-9y3 = x + -8xy + -6x3

Add '9y3' to each side of the equation.
-9y3 + 9y3 = x + -8xy + -6x3 + 9y3

Combine like terms: -9y3 + 9y3 = 0
0 = x + -8xy + -6x3 + 9y3

Simplifying
0 = x + -8xy + -6x3 + 9y3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}

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